Modifier is disabled skipping apply messsage
You are probably in "edit mode." You can't apply modifiers in edit mode, and the orange selection outline goes away in edit mode.

Blender organizes "meshes" into "objects". An "object" is a container that contains a "mesh". You can edit the mesh or the object, but not both at the same time. When you're dragging individual points around, you're editing the mesh (in edit mode). When you have the orange selection outline and you're dragging whole objects around, you're in object mode (and you can't drag individual points).

To toggle back and forth between edit (mesh) mode and object mode, press tab.

To apply your Boolean modifier tab until you're in object mode, then select the object that has the modifier you want to apply, and the "apply" button should now be available.

Like Nate said, you only need a Boolean modifier on one of the objects, but experimenting with it is the best way to figure out how that works.